The annual data for Brazil’s real GDP, capital, labour and different types of energy consumptions in the period between 1980 and 2010 was used to estimate the production models of Eq. (2), and to test for the multivariate cointegration and the Granger causality ofEq. (3).
4.1. Results of unit roots and co-integration tests
The time series properties of the variables in Eq. (2) are evaluated through three different unit root tests, namely ADF, PP, and KPSS. Each of the seven time series appears to contain a unit root in their levels but are stationary in their first difference, indicating that they are integrated at order one, i.e., I(1). The results are displayed inTable 2.
The next step is to test whether the variables in Eq. (2) are cointegrated. The results for the Johansen test using no lags and intercepts in the model are shown in Table 3. The trace and eigenvalue tests reject the hypothesis of no cointegrating equation
at a 5% level of significance for Eq.(2). The results in panels A–D of Table 3indicate the existence of at least one cointegrating vector for (LGDP, LGCF, LLF, LECi) combinations at the 5% significance level, where LECi; i¼1,…,4 are LNHREC, LTREC, LNREC, and LTEC, respectively. The resulting parameter estimates for Eq. (2) are reported inTable 4. The model properties are evaluated using two diagnostic tests, the Jarque and Bera (JB) test[38]for normality and the Ramsey RESET test[39]for functional form misspeci fica-tion. The test results reported inTable 4show that all models pass the diagnostic tests, indicating no significant deviations from the desired model properties. Thus, Eq.(2)is suitable for each type of energy consumption. That is, real GDP, capital formation, labour force, and each of the four type’s energy consumption share a common trend in the long run.
As far as the results of four cointegration vectors normalised on GDP are concerned, the coefficients of LGCF and LLF are found to affect the level of development significantly and positively by approximately 0.37% and 0.60% on average, respectively. This suggests that the process of economic development is heavily dependent on investment and labour in Brazil. The coefficients of NHREC and TREC are positive and significant, while the coeffi-cients of NREC and TEC are far from significant. A 1% increase in non-hydro renewable energy consumption increases real GDP by 0.06%, and a 1% increase in total renewable energy consumption increases real GDP by 0.20%. This suggests that renewable energy consumption is more sensitive to real output, while the impact of non-renewable or total primary energy consumption on real output is very small. Our findings highlight the importance of Table 3
Results of Johansen’s cointegration test.
Panel A: LGDP, LNHREC, LGCF, and LLF variables; no lags
Eigenvalue Trace stat. 5% critical value Max Eigen. stat. 5% critical value Number of co-integrations
0.92 114.67nnn 54.08 76.28nnn 28.59 None
0.50 38.40nn 35.19 20.76nn 22.30 At most 1
0.30 17.64 20.26 10.52 15.89 At most 2
Panel B: LGDP, LTREC, LGCF, and LLF variables; no lags
0.90 99.05nnn 54.08 69.93nnn 28.59 None
0.50 29.12 35.19 20.77 22.30 At most 1
Panel C: LGDP, LNREC, LGCF, and LLF variables; no lags
0.90 105.91nnn 54.08 68.82nnn 28.59 None
0.55 37.09nn 35.19 24.17nn 22.30 At most 1
0.27 12.92 20.26 9.41 15.89 At most 2
Panel D: LGDP, LTEC, LGCF, and LLF variables; no lags
0.90 100.51nnn 54.08 69.19nnn 28.59 None
0.45 31.32 35.19 17.89 22.30 At most 1
Note: The optimal lag lengths are selected using AIC. nnDenote significance on the 5% level.
nnnDenote significance on the 1% level.
Table 4
Coefficients of Eq.(2)for different types of energy consumption, 1980–2010.
LGCF LLF LNHREC LTREC LNREC LTEC Intercept R2 JB RESET
0.343*** 0.554*** 0.057** 2.301*** 0.9910 0.76 1.02
(9.02) (7.94) (2.13) (6.50) [0.68] [0.32]
0.365*** 0.434*** 0.201** 1.710*** 0.9912 1.49 0.73
(12.24) (3.96) (2.42) (16.24) [0.48] [0.40]
0.409*** 0.731*** −0.035 1.397*** 0.9897 1.55 1.25
(11.52) (12.48) (−0.72) (5.22) [0.46] [0.28]
0.395*** 0.694*** −0.001 1.571*** 0.9895 1.33 1.75
(10.77) (6.92) (−0.02) (4.21) [0.51] [0.20]
Note: Figures in parenthesis indicate t statistics. p-Values are reported in brackets. nnDenote significance on the 5% level.
nnnDenote significance on the 1% level.
Table 2
Results of unit roots tests, 1980–2010.
Variable ADF PP KPSS
Level 1st diff. Level 1st diff. Level 1st diff.
LGDP 1.19 −3.79a 1.79 −4.73a 2.46a 0.24
LGCF −0.19 −4.92a −0.06 −5.07a 2.29a 0.21
LLF −0.65 −4.75a −0.73 −4.75a 0.25a 0.05
LNHREC 1.53 −4.77a −1.75 −4.77a 2.08a 0.34
LTREC −1.01 −5.64a −1.04 −5.63a 1.80a 0.13
LNREC −0.53 −7.79a −0.26 −7.94a 0.80a 0.09
LTEC −0.68 −7.25a −0.26 −7.42a 2.42a 0.06
Note: The nulls of all tests except for the KPSS are unit roots. The null of KPSS states that the variable is stationary. Individual intercepts are included in test regressions.
aMeans that the null of the unit root test is rejected at a 1% level.
renewable energy sources within the Brazilian energy portfolio.
Brazil’s elasticity of real GDP to renewable energy consumption is greater than that found by Apergis and Payne[22]for Eurasia, and lower than those found by Apergis and Payne [23] for Central American countries as a whole.
4.2. Results of Granger causality tests
Cointegration implies the existence of causality, at least in one direction. However, it does not indicate the direction of the causal relationship. Hence, to shed light on the direction of causality,
Table 7
Results of causality tests for non-renewable energy consumption model.
Source of causation (independent variables)
Short-run Chi-square-statistics Long-run t statistics
ΔLGDP ΔLNREC ΔLGCF ΔLLF ECT
ΔLGDP 2.81 7.90nn 12.62nnn 1.40 (0.17)
ΔLNREC 1.58 13.02nnn 35.94nnn −8.23nnn(−0.54)
ΔLGCF 12.86nnn 3.44 1.44 −3.04nnn(−0.56)
ΔLLF 23.84nnn 21.29nnn 28.66nnn 4.25nnn(0.11)
Note: The optimal lag lengths are selected using AIC. Figures in parentheses are coefficients. nnIndicate 5% level of significance.
nnnIndicate 1% level of significance.
Table 8
Results of causality tests for total primary energy consumption model.
Source of causation (independent variables)
Short-run Chi-square-statistics Long-run t statistics
ΔLGDP ΔLTEC ΔLGCF ΔLLF ECT
ΔLGDP 0.23 10.02nnn 1.67 −1.18 (−0.08)
ΔLTEC 18.03nnn 7.64nn 35.58nnn −5.24nnn(−0.86)
ΔLGCF 5.51n 0.37 4.00 −1.32 (−0.44)
ΔLLF 38.41nnn 35.15nnn 42.06nnn 7.99nnn(0.21)
Note: The optimal lag lengths are selected using AIC. Figures in parentheses are coefficients. nIndicate 10% level of significance.
nnIndicate 5% level of significance.
nnnIndicate 1% level of significance.
Table 6
Results of causality tests for total renewable energy consumption model.
Source of causation (independent variables)
Short-run Chi-square-statistics Long-run t statistics
ΔLGDP ΔLTREC ΔLGCF ΔLLF ECT
ΔLGDP 1.70 8.51nn 1.69 −2.41nn(−0.16)
ΔLTREC 3.16 12.03nnn 7.39nn −6.07nnn(−0.04)
ΔLGCF 12.40nnn 3.37n 15.82nnn −3.36nnn(−0.67)
ΔLLF 12.05nnn 1.07 11.81nnn −0.43 (−0.02)
Note: The optimal lag lengths are selected using AIC. Figures in parentheses are coefficients. nIndicate 10% level of significance.
nnIndicate 5% level of significance.
nnnIndicate 1% level of significance.
Table 5
Results of causality tests for non-hydroelectric renewable energy consumption model.
Source of causation (independent variables)
Short-run Chi-square-statistics Long-run t statistics
ΔLGDP ΔLNHREC ΔLGCF ΔLLF ECT
ΔLGDP 42.83nnn 58.59nnn 9.44nn −11.40nnn(−0.55)
ΔLNHREC 23.01nnn 21.44nnn 14.47nnn −0.75 (−0.12)
ΔLGCF 0.14 2.88 3.67 −3.48nnn(−0.97)
ΔLLF 9.20nn 1.83 15.49nnn 0.60 (0.03)
Note: The optimal lag lengths are selected using AIC. Figures in parentheses are coefficients. nnIndicate 5% level of significance.
nnnIndicate 1% level of significance.
ECM-based causality tests are performed. Tables 5–8 report the causality results from estimating the vector error correction model for LGDP, LGCF, LLF, and four different types of energy consump-tion. Both the short-run Chi-square statistics and the long-run t statistics are shown for each ECM. The results reported inTable 5 indicate a bidirectional causality between NHREC and economic growth, and unidirectional causality from capital formation and labour force to NHREC in the short run. As for the long-run, there is unidirectional causality from NHREC to economic growth and bidirectional causality between economic growth and capital formation. Indeed, the short- and long-run Granger causality between economic growth and NHREC is partially similar to the previous research by Sadorsky[17]for 18 emerging countries as a whole and Apergis and Payne’s[21]results for OECD countries as a whole. The results of Table 6 indicate unidirectional short-run causalities from capital formation and labour force to TREC, and bidirectional causality between capital formation and TREC in the long-run. There also exists bidirectional causality between eco-nomic growth and TREC in the long-run, but no short-run causal relationship between them. This result is partially similar to those reported by Apergis and Payne [22,23] for Eurasia or Central American countries as a whole. As a result, the different causality relationship between NHREC-output and TREC-output is due to the NHREC that only accounts for 3.28% of the TREC during 1980– 2010. The overallfindings of bidirectional causality between NHREC and economic growth in the short-run, unidirectional causality from NHREC to economic growth and bidirectional causality between economic growth and TREC in the long-run highlight the importance of renewable energy sources within the energy port-folio of Brazil. Likewise, economic growth is crucial in providing the necessary resources for the sustainable development.
Table 7reports the causality results obtained from considering NREC. FromTable 7, the short-run dynamics suggest unidirectional causality from capital formation to NREC and bidirectional caus-ality between NREC and labour force. The ECT is statistically significant at the 1% level in capital formation, labour force, and NREC equations. This suggests that there is bidirectional causality between both NREC and capital formation and between NREC and labour force, and unidirectional causality from economic growth to NREC without feedback in the long-run. Comparing the results of Tables 7and8show that there is bidirectional causality between economic growth and total renewable energy consumption, but no causality running from non-renewable energy consumption to economic growth. As for the long-run, the magnitudes of the adjustment coefficients are −0.16 for the real GDP equation in Table 6. Thus, near-complete adjustments to the long-run equili-brium induced by changes in real GDP would take approximately 6 years after a shock occurs.
At the aggregate level, the causality results for TEC shown in Table 8suggest that unidirectional short-run causality from capital formation and economic growth to TEC and bidirectional causality between TEC and labour force. The ECT is statistically significant at the 1% level in both the labour force and TEC equations. This suggests that there is bidirectional causality between TEC and labour force, and unidirectional causality from economic growth and capital formation to TEC in the long-run. The bidirectional short- or long-run causality between NREC/TEC and labour force and the lack of either short- or long-run causality running from NREC/TEC to economic growth suggest that Brazil is an energy-independent economy. Indeed, after the world’s second oil-price shock, the Brazilian government has undertaken an ambitious programme to reduce its dependence on imported oil. At the
Fig. 3. CUSUM and CUSUMSQ plots for the estimated ECM of NHREC.
beginning of the 21st century, Brazil switched from being a large oil importer to almost being oil independent. Thus, Brazil’s economy is no longer dependent on foreign oil supply.
In testing for parameter constancy in each ECM model, we employed the CUSUM and CUSUMSQ tests to the estimated equations for which there were significant ECT. For the ECM with NHREC variable, the ECTs in the GDP and GCF equations are significant. The CUSUM and CUSUMSQ plots for each equation are shown inFig. 3. For the ECM with TREC variable, the ECTs in the GDP, TREC, and GCF equations are significant. For the ECM with NREC variable, the ECTs in the NREC, GCF, and LF equations are significant. For the ECM with TEC variable, the ECTs in the TEC and LF equations are significant.Figs. 4,5, and6show the CUSUM and CUSUMSQ plots of these equations. As seen, neither the CUSUM nor the CUSUMSQ test statistics exceeds the bounds of the 5% level of significance, indicating an overall constancy in the regression equations.